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1

Thermo-diffusion MHD convection in enclosure using heat and mass lines visualization techniques

Kushawaha Durgesh, Yadav Sushil, Singh Dwesh K., Behera Pravata Kumar

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

63--76

EN

The numerical study of two-dimensional laminar thermo-diffusion natural convection in an exponentially heated and concentrated square enclosure of unit length in the presence of a uniform horizontal magnetic field is presented in this paper. The left and right vertical walls are assumed to have higher and lower temperatures and concentrations, respectively, and are governed by exponential functions, whereas the horizontal walls are assumed to be adiabatic and non-diffusive. The mathematical formulation of heat and mass functions has been completed, and heat and mass line contours have been drawn based on these functions to investigate the behavior of heat and mass in the cavity. The flow governing equations were solved using a finite difference method in conjunction with the Successive Over-Relaxation (SOR) technique and then converted to a vorticity-stream function form. A detailed comparison of isotherms with heatlines and isosolutes with masslines has been performed. Furthermore, the reduction for lower Rayleigh numbers Ra surpassing the reduction for higher values of Ra. The maximum reduction in overall heat and mass transfer has been observed for higher Hartmann (Ha = 8).

2

Analysis of laminar and turbulent natural, mixed and forced convection in cavities by heatlines

Hernández-López I., Xamán J., Álvarez G., Chávez Y., Arce J.

Archives of Mechanics

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2016

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Vol. 68, nr 1

27--53

EN

Laminar and turbulent convective heat transfer in a ventilated and non-ventilated cavity was analyzed by heatlines. Heatlines show that in non-ventilated cavities it is possible to estimate the energy path using the streamlines for turbulent flow regime. In ventilated cavities, heatlines allow to observe that thermal energy travels along the top, by the bottom or by both paths due to the inertial force, the buoyant force or a combination of both, respectively. In the laminar regime, these situations are well established for the Rayleigh number (Ra). Nevertheless, in the turbulent regime, it was found that the combined effect of the inertial and buoyant forces on the energy path is disrupted when Ra > 109. Furthermore, heatlines in conjunction with temperature and velocity profiles allow to see that natural convection is preferred when cooling is required, while the forced convection is a better choice if heating is needed.

3

Numeryczna wizualizacja linii przepływu ciepła i gęstości strumienia ciepła w płaskim przewodzeniu ciepła metodą elementów brzegowych

Teleszewski T. J.

Modelowanie Inżynierskie

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2014

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T. 20, nr 51

116--122

PL

W publikacji przedstawiono algorytm metody elementów brzegowych (MEB) wyznaczania linii przepływu ciepła w płaskim przewodzeniu ciepła metodą elementów brzegowych. Prezentowany algorytm stanowi alternatywę wobec najczęściej stosowanych obszarowych metod numerycznych, takich jak metoda różnic skończonych, metoda objętości skończonych, metoda elementów skończonych. W metodach tych stosowane są pracochłonne i skomplikowane siatki wewnątrz obszaru, natomiast metoda elementów brzegowych wymaga jedynie dyskretyzacji brzegu. Weryfikacja algorytmu została wykonana na podstawie znanych rozwiązań teoretycznych. W pracy przedstawiono przykład obliczeniowy przepływu ciepła przez dwa przewody centralnego ogrzewania obudowane wspólną izolacją cieplną. W celu wykonania symulacji komputerowych został napisany autorski program obliczeniowy.

EN

The paper presents the numerical application of boundary element method (BEM) to calculate the heatline and heat flux density in two-dimensional steady state thermal conduction. The efficiency and the credibility of proposed algorithm were verified by numerical tests and the BEM solution is compared with theoretical results of steady state conduction in a plane wall with no heat generation and constant thermal conductivity. Numerical example is presented to illustrate steady state conduction in thermal isolation with a two pipe system of central heating. The BEM algorithm is an alternative to mesh method: Finite Difference Method, Finite Element Method or Finite Volume Method. The computer program was written in Fortran programming languages.